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Chapter 2: Q. 2.84 (page 69)

Use the specified grouping method to

Part (a): Determine a frequency distribution.

Part (b): Obtain a relative frequency distribution.

Part (c): Construct a frequency histogram based on your result from part (a).

Part (d): Construct a relative frequency histogram based on your result from part (b).

The U.S. Energy Information Administration collects data on residential energy consumption ad expenditures. Results are published in the document Residential Energy Consumption Survey: Consumption and Expenditures. The following table gives one year's energy consumption for a sample of 50 households in the South. Data are in millions of BTUs. Use limit grouping with a first class of 40-49 and a class width of 10.

Short Answer

Expert verified

Part (a): A frequency distribution is given below,


Part (b): A relative-frequency distribution is given below,

Part (c): On constructing a histogram using part (a), we get,

Part (d): On constructing a relative frequency histogram using part (b), we get,

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given question,

02

Part (a) Step 2. Determine a frequency distribution.

We know that limit grouping with a first class of 40-49 and a class width of 10.

As we are grouping by 10s and the shortest consumptions is 45, our firts class is 40-49, that is the energy consumption from 40million BTUS upto and including 49million BTUs.

The frequency distribution using single-value grouping is given below,

03

Part (b) Step 1. Determine the relative-frequency distribution.

The formula of the relative frequency is Relativefrequency=FrequencyNumberofobservations.

The relative frequency distribution is given below,

04

Part (c) Step 1. Construct a frequency histogram.

On constructing a histogram using part (a) is given below,

We can see that the given data is not symmetric.

05

Part (d) Step 1. Construct a relative frequency histogram.

On constructing a relative frequency histogram using part (b) is given below,

We can see that the given data is not symmetric.

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